A path is a finite sequence of vertices (not necessarily distinct) such that any two consequent vertices are connected by an edge. A path is passing through an edge if the edge connects a pair of consequent vertices of the path. A cycle is a path such that its first and its last vertex is the same. The length of a path is the number of the edges that the path is passing. On this page, we consider only graphs without parallel edges (two or more edges that are incident to the same two vertices). A path can be uniquely determined by the sequence of its vertices, but sometimes it is handy to include edges into the notation.